Filters are essential RFIC components for selecting a target frequency spectrum and suppressing spectral components at image frequencies. Although filters have been researched for decades, state-of-the-art technologies have serious shortcomings that have proven difficult to overcome. For example, lumped element filters cannot be used at frequencies above X band (˜8.0-12.0 GHz), and distributed filters suffer from a large footprint and are therefore hard to integrate on-chip monolithically. In addition, the performance of state-of-the-art filters may be severely limited by substrate losses caused by electric and magnetic couplings between the resonator and substrate.